Postbuckling of elastic beam subjected to a concentrated moment within the span length of beam

作     者：BoonchaiPhungpaingam SomchaiChucheepsakul 

作者机构：Department of Civil EngineeringFaculty of EngineeringKing Mongkut's University of Technology ThonburiPracha-utid RdBangmodToongkruBangkok10140Thailand 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2007年第23卷第3期

页      面：287-296页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Thailand Research Fund TRF: PHD/ 0045/2548 

主　　题：Postbuckling Elastica Concentrated moment Elliptic integral Shooting method 

摘      要：This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment within the span length of beam. Two approaches are used in this paper. The non-linear governing differential equations based on elastica theory are derived and solved analytically for the exact closed form solutions in terms of elliptic integral of the first and second kinds. The results are presented in graphical diagram of equilibrium paths, equilibrium configurations and critical loads. For validation of the results from the first approach, the shooting method is employed to solve a set of nonlinear differential equations with boundary conditions. The set of nonlinear governing differential equations are integrated by using Runge-Kutta method fifth order with adaptive step size scheme. The error norms of the end conditions are minimized within prescribed tolerance （10^-5）. The results from both approaches are in good agreement. From the results, it is found that the stability of this type of beam exhibits both stable and unstable configurations. The limit load point existed. The roller support can move through the hinged support in some cases of β and leads to the more complex of the configuration shapes of the beam.